Introduction:
The maximum distance and height to which a person can throw a stone are determined by various factors such as the initial velocity, launch angle, air resistance, and gravitational force. To solve this problem, we need to consider the projectile motion of the stone.

Projectile Motion:
Projectile motion refers to the motion of an object that is launched into the air and moves under the influence of gravity. It follows a curved trajectory, consisting of both horizontal and vertical components. The maximum distance and height occur at specific launch angles.

Maximum Distance:
The maximum distance is achieved when the stone is launched at an angle of 45 degrees. At this angle, the horizontal and vertical components of the initial velocity are equal. The stone will travel the farthest horizontally before hitting the ground. Therefore, the person can throw the stone to a maximum distance of 100m.

Maximum Height:
The maximum height occurs when the stone is launched vertically upwards (angle of 90 degrees). In this case, the initial velocity only has a vertical component. The stone will reach its peak height before falling back down. The vertical distance achieved will be equal to the maximum height. Therefore, the person can throw the stone to a maximum height of 100m.

Other Options:
The person will not be able to throw the stone to a greater height than the maximum distance. Therefore, options 1) 100m and 2) 75m are not valid answers.

Conclusion:
Based on the principles of projectile motion, the person can throw the stone to a maximum distance of 100m and a maximum height of 100m. The launch angle of 45 degrees will result in the maximum distance, while launching vertically upwards (90 degrees) will achieve the maximum height.

As you know max. Range = u^2/g
max. height = u^2/2g
therefore, max. height = 100/2 = 50